Question

17and 18 please help me to do this

Answer 1

17) Let the number be x

=> 20% increase =

$(\frac{20}{100} \times x )+ x \\ \\ = > \frac{x}{5} + x \\ \\ = > \frac{x}{5} + \frac{5x}{5} \\ \\ = > \frac{6x}{5}$

Now it is decreased by 20%

=>
$\frac{6x}{5} - ( \frac{20}{100} \times \frac{6x}{5} ) \\ \\ = > \frac{6x}{5} - \frac{6x}{25} \\ \\ = > \frac{30x}{25} - \frac{6x}{25} \\ \\ = > \frac{24x}{25}$

Since,

x > 24x/25

The percentage here is overall decreased

Percent decreased =
$(x - \frac{24x}{25}) \div x \times 100 \\ \\ = > ( \frac{25x}{25} - \frac{24x}{25} ) \times \frac{1}{x} \times 100 \\ \\ = > \frac{x}{25} \times \frac{1}{x} \times 100 \\ \\ = > 4\%$


So overall decreased = 4%


18) Again, let the number be x

So 40% decreased

=
$x - ( \frac{40}{100} \times x) \\ \\ = > x - \frac{2x}{5} \\ \\ = > \frac{5x}{5} - \frac{2x}{5} \\ \\ = > \frac{3x}{5}$

Now again 60% decreased

=>
$\frac{3x}{5} - ( \frac{60}{100} \times \frac{3x}{5} ) \\ \\ = > \frac{3x}{5} - \frac{9x}{25} \\ \\ = > \frac{15x}{25} - \frac{9x}{25} \\ \\ = > \frac{6x}{25}$


since, x > 6x/25 Their is a decrease

so percentage decreased =
$(x - \frac{6x}{25} ) \div x \times 100 \\ \\ = > ( \frac{25x}{25} - \frac{6x}{25} ) \times \frac{1}{x} \times 100 \\ \\ = > \frac{19x}{25} \times \frac{1}{x} \times 100 \\ \\ = > 76\%$


Your answer = 76% decreased